Visit any inn and ask the innkeeper if they have heard any rumors. They will tell you that a wizard in Morthal named Falion studies vampires. Travel to Morthal and meet with him. He will ask you to bring him a Black Soul Gem (you can buy one from him for 880 septims). To fill the black soul gem you must cast Soul Trap or use a weapon enchanted with soul trap on an NPC (man, mer, beast race, etc...) and then kill them to get their soul. Once filled, take it to Falion and he will instruct you to meet him at a summoning circle just outside of town at dawn (at around 5am). Once there, he will perform a short ceremony and your vampirism will be cured. Note that you must not be at stage 4 vampirism, otherwise Falion will refuse to perform the ritual.

You can also cure your Vampirism by becoming a werewolf within the Companions faction. However, once you contract Lycanthropy you gain a 100% resistance to disease and cannot be re-infected with Sanguinare Vampiris.